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On Identities and m-Neutral Sequences of n-Ary Groups


In this paper, we study such polyadic analog of an identity of a group as m-neutral sequence. In particular, we prove that all Post’s equivalence classes of the free covering group of any n-ary group [where \(n = k(m - 1) + 1\) and \(k\ge 1\)] defined by m-neutral sequences form the \((k + 1)\)-ary group, which is isomorphic to the n-ary subgroup of all identities of the n-ary group in the case when \(m = 2\).

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Correspondence to Viktoria A. Kovaleva.

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Gal’mak, A.M., Kovaleva, V.A. On Identities and m-Neutral Sequences of n-Ary Groups. Commun. Math. Stat. 4, 495–508 (2016).

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  • n-Ary group
  • Identity
  • m-Neutral sequence

Mathematics Subject Classification

  • 20N15